Studies in Chemical Process Design and
Synthesis:
Part V: A Simple Heuristic Method for Systematic Synthesis of Initial
Sequences for Multicomponent Separations
A simple heuristic method for the systematic synthesis of initial sequences for
multicomponent separations is proposed and applied to a number of synthesis
problems which have been solved previously using other methods. Based on reported costs, it is shown that the initial sequences synthesized for the test problems
by the new heuristic method are cheaper than those obtained by other ordered
heuristic methods. These initial sequences are also either identical to or at most
a few percents higher in costs than those optimum sequences obtained by other
algorithmic, heuristic-algorithmic and heuristicevolutionary methods. The new
method is straightforward to apply by hand and it does not require any mathematical background and computational skill from the user.
V. M. NADGIR
Department of Chemical Engineering
Auburn University
Auburn Universlty, AL 36849
and
Y. A.
LIU
Department of Chemical Engineering
Virginia Polytechnic Institute and
State University
Blacksburg, VA 24061
SCOPE
An important process design problem is the systematic synthesis of multicomponent separation sequences which is concerned with the systematic selection of the method and sequence for separating a multicomponent mixture into several
products of relatively pure species. The general techniques
which have been developed for solving the separation sequencing problem have included: algorithmic approaches involving some established optimization principles (e.g., Hendry
and Hughes, 1972); heuristic methods based on the use of rules
of thumb (e.g., Rudd et al., 1973, pp. 155-208); evolutionary
strategies wherein improvements are systematically made to
an initially created separation sequence (e.g., Stephanopoulos
and Westerberg, 1976); and thermodynamic methods involving
applications of thermodynamic principles (e.g., Hohmann et
al., 1980). In some situations, two or more of these techniques
have been used together in the synthesis (e.g., Seader and
Westerberg, 1977). A review of previous studies on multicomponent separation sequencing can be found in Nishida et al.
(1981).
A disadvantage of many existing algorithmic and evolutionary techniques as reviewed by Nishida et al. is that their applications require special mathematical background and computational skill from the user. Although heuristic rules to guide the
order of separation sequencing have long been available, many
of the known heuristics contradict or overlap others; and procedures to resolve these conflicts have not been adequately
developed. Recently, some success has been reported on the
applications of certain heuristics together with evolutionary
strategies for multicomponent separation sequencing (Seader
and Westerberg, 1977; Nath and Motard, 1981).
In this work, a simple heuristic method for the systematic
synthesis of initial sequences for multicomponent separations
is proposed. A comparison of the new heuristic method with
other recent methods, particularly the heuristicevolutionary
methods by Seader and Westerberg (1977) and by Nath and
Motard (1981), is presented. A number of illustrative examples
are given to demonstrate the simplicity and effectiveness of the
proposed method.
CONCLUSIONS AND SIGNIFICANCE
This work proposes and demonstrates a simple heuristic
method for the systematic synthesis of initial sequences of
multicomponent separations. The new method involves the
sequential applications of the following seven heuristics: (1)
favor ordinary distillation and remove mass separating agent
first; (2) avoid vacuum distillation and refrigeration; (3)favor
the smallest product set; (4) remove corrosive and hazardous
components first; (5) perform difficult separations last; (6)remove the most plentiful component first; and (7)favor equimolal
(50/50) split. The first two heuristics decide the separation
methods to be used. The next three heuristics give guidelines
about the forbidden splits due to product specifications, as well
as the essential first and last separations. The last two heuristics
are used to synthesize the actual initial separation sequences,
Correspondenceconcerning this paper should be addressed to Y. A. Liu.
Page 926
November, 1983
with the help of an auxiliary sequencing parameter, called the
coefficient of ease of separation (CES)(Eq. 1).
The new heuristic method has been applied to a number of
synthesis problems which have been solved previously using
other methods. Based on reported costs for the illustrative examples presented, it is shown that the initial sequences synthesized by the new heuristic method are cheaper than those
obtained by other ordered heuristic methods of Seader and
Westerberg (1977) and of Nath and Motard (1981). These initial
sequences are also either identical to or at most a few percents
higher in costs than those optimum sequences obtained by other
algorithmic (e.g., Hendry and Hughes, 1972), heuristic-algorithmic (e.g., Thompson and King, 1972), and heuristicevolutionary (Seader and Westerberg, 1977; Nath and Motard, 1981)
methods.
The new heuristic method offers the advantages of simplicity
AlChE Journal (Vol. 29, No. 6)
and effectiveness, coupled with good performance. Further, the
new method is straightforward to apply by hand and it does not
require any mathematical background and computational skill
from the user.
INTRODUCTION
or relative volatility of the key components CYLK,HK <LO5 (Van
Winkle, 1967, p. 381; Seader, and Westerberg, 1977)to 1.10(Nath
Multicomponent separation systems are found in widespread
use in the chemical and petroleum industries. An important process
design problem in multicomponent separations is the separation
sequencing, which is concerned with the selection of the optimal
method and sequence for the separation. This problem is often
solved by first arranging the components in the mixture to be
separated in some ranked lists of appropriate physical and/or
chemical properties such as relative volatility or solubility in water.
The resulting ranked list for each property gives the component
name and its property ranking relative to other components in the
mixture. This list also allows a separation step to be considered as
a list splitting operation, in which components above a certain
property value are separated from components below that
value.
The generation of a separation sequence then involves the selection of an appropriate property list and the choice of separation
keys within the list. For example, sequences for separating a
three-component mixture of A , B and C into pure components by
two ordinary distillation columns can be found by first arranging
the components in a ranked list of relative volatility from most
volatile ( A )to least volatile (C),and then examining the different
splits in the two columns. One possible sequence involves making
the split A/BC in the first column followed by the split B/C in the
second column. Another possible sequence corresponds to making
the split A B / C in the first column and the split A / B in the second
column. %me excellent discussion of the background information
related to the separation sequencing problem can be found in the
textbooks by Rudd et al. (1973, pp. 155-208 and 288-295), King
(1980, pp. 71&720), and Henley and Seader (1981, pp. 527-555).
A review of previous studies on the subject can be found in Nishida
et al. (1981).
and Motard, 1981), the use of ordinary distillation is not recommended. A MSA may be used, provided that it improves the relative volatility between the key components. (b) When a MSA is
used, remove it in the separator immediately followingthe one into
which it is used (Hendry and Hughes, 1972;Rudd et al., 1973, pp.
174-180; Seader and Westerberg, 1977).
2. Heuristic M2 (Avoid Vacuum Distillation and Refrigeration). All other things being equal, avoid excursions in temperature
and pressure, but aim higher rather than lower (Rudd et al., 1973,
pp. 182-183). If vacuum operation of ordinary distillation is required, liquid-liquid extraction with various solvents might be
considered. If refrigeration is required (e.g., for separating materials of low boiling points with high relative volatilities as distillate
products), cheaper alternatives to distillation such as absorption
might be considered (Sounders, 1964; Seader and Westerberg,
1977; Nath and Motard, 1981).
3. Heuristic D1 ( F a m Smulkst Product Set). Favor sequences
which yield the minimum necessary number of products. Equivalently, avoid sequences that separate components which should
ultimately be in the same product (Thompson and King, 1972;
King, 1980, p. 720). In other words, when multicomponent products are specified, favor sequences that produce these products
directly or with a minimum of blending unless relative volatilities
are appreciably lower than those for a sequence which requires
additional separators and blending (Seader and Westerberg, 1977;
Henley and Seader, 1981, p. 541).
4. Heurtktic S 1 (Remove Corrosive and Hazardous Components First). Remove corrosive and hazardous materials first (Rudd
eta]., 1973, p. 170).
5. Heuristic S2 (PerformDifficult Separations Last). All other
things being equal, perform the difficult separationslast (Harbert,
1957; Rudd et al., 1973, pp. 171-174). In particular, separations
where relative volatities of the key components are close to unity
should be performed in the absence of nonkey components. In
other words, try to select sequences which do not cause nonkey
components to be present in separationswhere the key components
are close together in relative volatility or separation factor (Heaven,
1969; King, 1980, p. 715).
6. Heuristic C1 (Remove Most Plentiful Component First).
A product composing a large fraction of the feed should be separated first, provided that the separation factor or relative volatility
is reasonable for the separation (Nishimura and Hiraizumi, 1971;
Rudd et al., 1973, pp. 167-169; King, 1980, p. 715).
7. Heuristic C2 ( F u m Sol50 Split). If component compositions
do not vary widely, sequences which give a more nearly 50/50 or
equimolal split of the feed between distillate ( D )and bottoms ( B )
products should be favored, provided that the separation factor or
relative volatility is reasonablefor the split (Harbert, 1957; Heaven,
1969; King, 1980, p. 715). If it is difficult to judge which split is
closest to 50/50 and with a reasonable separation factor or relative
volatility,perform the split with the highest value of the coefficient
of ease of separation (CES)first.
The coefficient of ease of separation (CES)as proposed in heuristic C2 is defined as
A SIMPLE HEURISTIC METHOD
Essentially all of the reported heuristic rules for separation sequencing can be broadly classified into four categories: (1)method
heuristics (designated as M heuristics) which favor the use of
certain separation methods under given problem specifications;
(2) design heuristics (designated as D heuristics) which favor
specific separation sequences with certain desirable properties; (3)
species heuristics (designated as S heuristics) which are based on
the property differences between the species to be separated; and
(4) composition heuristics (designated as C heuristics) which are
related to the effects of feed and product compositions on separation costs. Note that these classificationsof heuristics are the same
as those described by Tedder (1975),except that the method heuristics as defined here are broader than Tedder’s “state” heuristics.
In what follows, a simple ordered heuristic method for the systematic synthesis of initial sequences for multicomponent separations is proposed. This method involves the systematicuse of the
following seven heuristics, which are to be applied one by one in
their given order. If any heuristic is not important in, or not applicable to, the synthesis problem, the next one in the method is
considered.
1. Heuristic M 1 (Favor Ordinary Distillation and Remove
Muss Separating Agent First). (a) All other things being equal,
favor separation methods using only energy separating agents (e.g.,
ordinary distillation), and avoid using separation methods (e.g.,
extractive distillation)which require the use of species not normally
present in the processing, i.e., the mass separating agent (MSA)
(Rudd et al., 1973,pp. 174-181). However, if the separation factor
AlChE Journal (Vol. 29, No. 6)
CES
= f xA
where f = the ratio of the molal flow rates of products (distillate
and bottoms) BID or D / B , depending on which of the two ratios,
BID and D / B , is smaller than or equal to unity; and A = AT =
boiling point difference between the two components to be separated, or A = (a - 1)x 100 with a being the relative volatility or
separation factor of the two components to be separated.
November, 1983
Page 927
TABLE1. COMPARISON OF THREESYNTHESIS METHODS FOR SEPARATION SEQUENCING
Heuristic-Evolutionary Method
(Seader and Westerberg, 1977)
Ordered Heuristic Method
(This Work)
1. Step 1: To decide the separation methods to
be used
(a) heuristics M l a and Mlb (favor ordinary
distillation and remove mass separating
agent first).
(b) heuristic M2 (avoid vacuum distillation
and refrigeration).
2. Step 2: To give guidelinesabout the forbidden
splits due to product specifications
(a) heuristic D1 (favor smallest product
set).
3. Step 3: To give guidelines about the essential
first separations
(a) heuristic S1 (removecorrosive and hazardous component first).
4. Step 4: To give guidelines about the essential
last separations
(a) heuristic S2 (perform difficult separations
last).
5. Step 5: To synthesize the actual initial separation sequence
(a) heuristic C1 (remove most plentiful
component first).
(b) heuristic C2 (favor 50/50 split)
(c) auxiliary sequencing parameter: CES
(coefficient of ease of separation)defined
by Eq. 1.
1. Step 1: To decide the separation methods to
be used
(a) heuristic Mla (favor ordinary distillation).
(b) heuristic M 2 (avoid vacuum distillation
and refrigeration).
2. Step 2: To synthesize the actual initial separation sequence
(a) heuristic S3a (perform easy separations
first).
(b) heuristic C1 (remove most plentiful
component first).
(c) heuristic 0 2 (direct sequence rule).
(d) auxiliary sequencing parameters: relative
volatility or separationfactor a and feed
molar percentage.
3. Steps la and 2a: To be applied together with
Steps 1 and 2 when separations with mass
separating agents are considered
(a) heuristic Mlb (remove mass separating
agent first).
(b) heuristic D1 (favor smallest product
set).
4. Step 3 local evolutionary improvement of the
initial separation sequence.
In applying the new method to separation sequencing, method
heuristics M1 and M2 first decide the separation methods to be
used. Design heuristic D1 and species heuristics S1 and S2 then give
guidelines about the forbidden splits due to product specifications,
as well as the essential first and last separations. Finally, the actual
initial sequences are synthesized by using composition heuristics
C1 and C2 with the help of the Coefficient of ease of separation
(CES).
Since CES jnvolves the relative volatility or separation factor
for the two components to be separated, the application of the new
heuristic method depends indirectly on the separation temperature
and pressure. A good correlation for the optimum overhead pressure ( P D ) as a function of the normal feed bubble point (TFB)in
ordinary distillation has been presented by Tedder and Rudd
(1978) as follows:
+
In PO = 1 , 7 5 1 / ( T ~ ~273) - 6.777
(2)
In Eq. 2, PD is in MPa and TFBin "C such that 0.007 < PD I6.89
and -72°C < T < 699°C. Also, a systematic procedure for specifying other operating pressures in ordinary distillation can be found
in Henley and Seader (1981, pp. 432-434).
COMPARISON WITH RECENT HEURISTIC-EVOLUTIONARY
METHODS
Table 1 compares the new heuristic method with two recent
heuristic-evolutionary methods by Seader and Westerberg (1977)
and by Nath and Motard (1981).The latter methods involve the
following steps: (a) generating an initial separation sequence by
using a n ordered heuristic method; (b)developing a set of evolutionary rules to modify the initial separation sequence; (c) adopting
a strategy to systematically apply the evolutionary rules; and (d)
comparing the initial and modified separation sequences by some
performance criteria such as separation costs.
The following additional heuristics have been included in the
two heuristic-evolutionary methods summarized in Table 1for the
generation of initial separation sequences.
8. Heuristic M l c (Remove Mass Separating Agent Properly).
A separation method using a mass separating agent (MSA) cannot
be used to isolate another MSA (Nath and Motard, 1981).
Page 928
November, 1983
Heuristic-EvolutionaryMethod
(Nath and Motard, 1981)
1. Step 1: To give guidelinesabout the forbidden
splits due to product specifications
(a) heuristic D1 (favor smallest product
set).
2. Step 2: To decide the separation methods to
be used
(a) heuristic Mla (favor ordinary distillation)
(b) heuristic Mlc (remove mass separating
agent properly).
(c) heuristic M2a (avoid vacuum distillation)
(d) auxiliary design heuristics: set the split
fractions of the key components to the
prespecified values; and set the operating
reflux ratio to 1.3 times the minimum
ratio for each distillation colqmn.
3. Step 3: To synthesize the actual initial separation sequence
(a) heuristic S3b (perform easy separations
first).
(b) Auxiliary sequencing parameter: CDS
(coefficient of difficulty of separation)
defined by Eq. 3.
4. Step 4: global evolutionary improvement of
the initial separation sequence
9. Heuristic 0 2 (Direct Sequence Rule). During distillation,
when neither the relative volatility nor the molar percentage in the
feed varies widely, remove the components one by one as distillate
products. The resulting sequence is commonly known as the direct
sequence, in which the optimum operating pressure tends to be
highest in the first separator and is reduced in each subsequent
separator (Lockhart, 1947; Harbert, 1957; Heaven, 1969; Rudd et
al., 1973,pp. 183-184; Seader and Westerberg, 1977; King, 1980,
p. 715).
10. Heuristic S3a (PerformEasy Separations First). Favor easy
separations first. Specifically, arrange the components to be separated according to their relative volatilities or separation factors
in a n ordered list. When the adjacent relative volatilities of the
ordered components in the feed vary widely, sequence the splits
in the order of decreasing adjacent relative volatility (Seader and
Westerberg, 1977).
11. Heuristic S3b (PerformEasy Separations First). Favor easy
separations first. Specifically, arrange the separations to split the
feed into the distillate and bottoms products in an increasing order
of the coefficient of difficulty of separation (CDS) defined by
D + B [*
(3)
where SPLK and S P H K are, respectively, the split fractions of the
light and heavy key components in the distillate and bottoms
products; D and B are, respectively, the molal flow rates of the
distillate and bottoms; and o ( L K , H K is the relative volatility of the
key components (Nath and Motard, 1981).
A number of differences among the three methods listed in Table
1 for the synthesis of initial separation sequences can be noted as
follows:
(1) In steps 1 and 2 of the ordered heuristic method by Nath
and Motard (1981), heuristic D1 (favor smallest product set)
overrides heuristic M l a (favor ordinary distillation). A consequence
of retaining the smallest product set is that sometimes a separation
method using a mass separating agent is chosen instead of ordinary
distillation. For example, consider the separation of a three-component mixture of A , B, and C into two products of (A$) and C
AlChE Journal (Vol. 29, No. 6)
by ordinary distillation (method I) and extractive distillation with
solvent X (method II), as described by Nath (1977).The rank lists
(RL) of decreasing adjacent relative volatility corresponding to
these two separation methods are given by:
RL(1):A C B
RL(I1):A B C X
The initial separation sequence resulting from applying steps 1 and
2 of the method by Nath and Motard is:
A
By contrast, the initial sequence obtained by applying steps 1 and
2 of the method presented in this work and that by Seader and
Westerberg (1977)is:
The separation sequencing by the new heuristic method is done
as follows.
(1) Heuristics M1 and M 2 : Use ordinary distillation with refrigeration at high pressure.
(2) Heuristics D1 and S1: Not applicable.
(3) Heuristic S2: Split DIE has the smallest relative volatility
of a = 1.25 compared to those of other splits. Therefore, it should
be done last in the absence of A , B and C .
(4) Heuristic C1: Although E is a large fraction of the feed, it
should not be separated first. This follows because the new heuristic
method is an ordered one, and the preceding heuristic S2 overrides
the present heuristic C1.
(5) Heuristic C2: For separatingABCDE, split ABCIDE is done
first since it has the largest CES of 114.50.To separate ABC, the
possible splits are A/BC and AB/C. By comparing the CESs for
the splits,
AIBC
f
0.05/0.40
100
12.5
( a - 1) x 100
CES
=A
0.20/0.25
33
26.4
it can be seen that AB/C is preferred over A/BC. Thus, the resulting sequence, which performs split DIE last, is:
This sequence favors the use of ordinary distillation (heuristic
Mla), instead of having the smallest product set (heuristic D l ) .
Also, in step 2 of the method by Nath and Motard, the heuristic of
avoiding refrigeration has not been included.
(2) The incorporation of steps 3 and 4 in the method presented
in this work represents an important difference of the new method
from those by Seader and Westerberg and by Nath and Motard.
These steps identify the essential first and last separationsby using
heuristics S 1 (remove corrosive and hazardous components first)
and S2 (perform difficult separations last) prior to the actual synthesis of the initial separation sequence. Also, the specific heuristics
and auxiliary separation sequencing parameters used by each
method for this synthesis of initial separation sequences are not
identical, as shown in Table 1.
(3) The last difference among the three methods is related to
the evolutionarystep. The method presented in this work is a purely
heuristic procedure and does not include an evolutionary step. Both
the methods by Seader and Westerberg and by Nath and Motard
include an evolutionary step, but with a different evolutionary
strategy. In the method by Seader and Westerberg, a local evolution
of the initial separation sequence is adopted; while in the method by
Nath and Motard, a global evolutionary strategy is used. This difference between the two evolutionarystrategies may be illustrated
by considering the change to be made to replace the separation
method for a specific separation task in an initial sequence. The
method of Seader and Westerberg does not change the initial
downstream structure (the separation methods for the remaining
separation tasks located downstream of the initial sequence). By
contrast, the method of Nath and Motard completely eliminates
the initial downstream structure and synthesizes a new sequence
by heuristics.
ILLUSTRATIVE EXAMPLES
Example 1: Separation of Llght Paraffins by Ordinary Distillation
Consider the separation of a mixture of five light hydrocarbons
into pure components by ordinary distillation studied by Heaven
(1969).The feed mixture is:
;\
D
Df
E---E
The second sequence can be systematically found by considering
the alternative splits in separating ABC, while retaining the best
initial split (according to CES)ABC/DE and also performing the
difficult split DIE last. Specifically, if split A/BC with the second
largest CES of 12.5 for separating ABC is done first, instead of
AB/C as in sequence la, a second sequence is found as follows:
A
A
&f
B f
(sequence lb)
EhE
Since other sequences with an initial split ABCIDE which satisfy
the constraints imposed by heuristics M1 to C l do not exist, the
third sequence is to be found by examining the alternative initial
splits for separating ABCDE. Although initial splits ABCDIE and
ABICDE have the second and third largest CES of 13.46 and 8.25,
respectively, these splits are not recommended because of the
constraint of performing the relatively difficult separations DIE
and B / C last according to heuristic S2. Therefore, the third sequence is found by choosing split AIBCDE first. The resulting
sequence which performs splits B / C and DIE last, is:
A
A
(sequence l c )
Relative
Volatilitya
Species
A:ProDane
B:i-Butane
C:n-Butane
D:i-Pentane
E:n-Pentane
A
Fraction
0.05
0.15
0.25
0.20
0.35
At 37.8% and 1.72 MPa
AlChE Journal (Vol. 29, No. 6)
N
2.00
1.33
2.40
1.25
CES
5.26
8.25
114.50
13.46
Table 2 compares the different sequences synthesized by the
three methods listed in Table 1, based on the detailed design and
costing reported by Heaven (1969). Sequence la corresponds to
November, 1983
Page 929
1
TABLE2. COMPARISON OF REPORTED SEQUENCES FOR EXAMPLE
Ordered Heuristic
SeCost
Method. This
cluence $/vra
Work
la
Initial Sequence
(Best)
863,580 2nd Sequence
(0.56%)b
871,460 3rd Sequence
(1.49%)
858,780
1b
lc
Heuristic-Evolutionary Methods
Seader &
WesterNath & Motard
berg (1977)
(1981)c
The resulting sequence, which performs splits C/D and E/F last,
is:
A
A
B f B
Final Sequence
(Best)
Initial Sequence
Initial and
Final Sequence
(Best)
a As reported by Heaven (1969)
b (0 56%)means that the cost of $863,58O/yr is 0 56%above the minimum cost of $858,78O/yr
for the best sequence reported by Heaven (1969)
As reported In Nath (1977)
the best sequence reported by Heaven (1969) using heuristics and
by Seader and Westerberg using their heuristic-evolutionary
method. Sequence l b corresponds to a nearly optimal sequence
with only 0.56%higher cost than sequence la. Sequences l a and
1b also correspond to two best sequences reported by Rathore, et
al. (1974) and by Gomez and Seader (1976), using optimization
methods.
This is exactly the same as the one presently being practiced in the
industry (Rudd et al., 1973, p. 185; King, 1980, p. 718).
The second sequence can be obtained by making the split
ABCDIEFC first (which has the second largest CES of 18.1 in
splitting ABCDEFG into two products) and performing the difficult splits C/D and EIF last as in the above sequence. This second
sequence is:
z(
Example 2: Separation of Products from Thermal Cracklng of
Hydrocarbons
Species
A:Hydrogen
B:Methane
C:Ethylene
D:Ethane
E:Propylene
F:Propane
G:Heavies
Moles/Hr
18
5
24
15
14
6
8
AT
-
CES
92
57
16
40
6
41
23.0
19.6
14.6
18.1
1.1
4.0
It is desired to separate the feed into the followingsix products: AB,
C, D, E, F and G. The separation sequencing by the new heuristic
method can be done as follows.
(1) Heuristics M 1 and M2: Use ordinary distillation with refrigeration at high pressure.
(2) Heuristic D1: Avoid splitting AB as it is a single product.
(3) Heuristic S1: Not applicable.
(4) Heuristic S2: Performs splits CID and EIF last due to their
small AT of 6 to 16°C.
(5) Heuristic C1: Not applicable.
(6) Heuristic C2: For separating ABCDEFG, the best split is
ABICDEFC which has the largest CES of 19.6 and also retains AB
as a single product:
For separating CDEFG, splits CID and EIF are performed last
so that the remaining splits to be chosen are CDIEFG and
CDEFIG. Split CDIEFG is done first since it has a larger CES of
28.7:
f
AT
CES
Page 930
CDIEFG
28/39
40
28.7
November, 1983
A
u
D b D
(sequence 2b).
- t i
Consider the multicomponent separations involved in the
large-scale thermal cracking of hydrocarbons to manufacture
ethylene and propylene (Rudd, et al., 1973, pp. 183-185; King,
1980, pp. 708-710). The feed mixture is:
Normal Boiling
Point, T ” C
-253
-161
-104
-88
-48
-42
-1
.
This sequence is used by the industry in the thermal cracking of
naphthas (King, 1980, p. 718).
Example 3A: Separation of Light Oieflns and Paraffins by Ordinary
Distillation
Consider the separation of a mixture of light olefins and paraffins
by ordinary distillation. The feed mixture as originally presented
by Thompson and King (1972) is:
Species
A:Ethane
B:Propylene
C:Propane
D:l-Butene
E:n-Butane
F:n-Pentane
Mole
Fraction
0.20
0.15
0.20
0.15
0.15
0.15
Relative
Volatilitya
a
CES
3.50
1.20
2.70
1.21
3.00
62.5
10.7
139.1
9.0
35.3
At 37 8°C and 0 I MPa
It is desired to find the sequences for separating the feed into pure
components,namely, A, B , C, D, E and F (Seaderand Westerberg,
1977; Nath, 1977). The separation sequencing by the new heuristic
method is done as follows.
(1) Heuristics M1 and M2: Use ordinary distillation with refrigeration at high pressure.
(2) Heuristics D1 and S1: Not applicable.
(3) Heuristic S2: Splits BIC and DIE are relatively difficult
separations due to their small values of relative volatility, a =
1.20-1.21. Thus, these splits should be done last.
(4) Heuristic C1: Not applicable since none of the components
represents a larger fraction of the feed.
(5) Heuristic C2: ABCIDEF represents a 55/45 split between
the distillate and bottoms and has a reasonable value of relative
volatility of a = 2.70 along with the largest value of CES of 139.1.
Therefore, this split should be dune first:
CDEFIG
8/59
41
5.6
AlChE Journal (Vol. 29, No. 6 )
TABLE3. COMPARISON OF REPORTED SEQUENCES FOR EXAMPLE
3A
A
+
A
Heuristic-Evolutionary Methods
Ordered
Heuristic
Se- Method, This
auence
Work
Seader &
Westerberg
(1977)
3a
Initial
Final Sequence
Sequence $1,153,000/yr
(Best)
3b 2nd
2nd Sequence
Sequence $1,213,000/yr
(5.2%)a
3c
3d
3e
Nath & Motard
(1981)b
2nd Sequence $685,189/yr
(8.7%)
Initial Sequence
$748,17S/yr (18.6%)
Final Sequence $630,454/
yr (Best)
3rd Sequence $805,105/yr
(27.7%)
Initial Sequence
$1,234,OOO/yr
(7.0%)
~
(5.2%) means that the cost of $1,213,MX)/yr is 5.2% above the minimum cost of $1,153,MX)/yr
for the best sequence reported in the same reference
As reported in Nath (1977)
a
The resulting sequence, which splits B/C and DIE last according
to heuristic S2, is:
The second sequence can be obtained by making split AIBCDEF
first (whichhas the second largest CES of 62.5 in splittingABCDEF
into two products) and performing the difficult splits B/C and DIE
last as in the above initial sequence. This sequence is:
(sequence 3b)
Table 3 compares the sequences synthesized by the three methods
summarized in Table 1. The additional sequences (3c to 3e) listed
in the table are as follows (Seader and Westerberg, 1977; Nath,
1977):
The costs tabulated in Table 3 and in subsequent examples should
be compared on a relative basis, as different annual costs were reported for the same sequences by different investigators. It is apparent that different assumptions and/or methods for design calculations and equipment costing might have been employed by
different investigators.
Table 3 shows that sequence 3a is cheaper than those obtained
by the ordered heuristic methods by Seader and Westerberg and
by Nath and Motard, namely, sequences 3e and 3b, respectively.
Sequences 3a and 3b also correspond to the best and second best
sequencesobtained by the heuristic-evolutionarymethod by Seader
and Westerberg. By applying a global evolutionary strategy to
modify the initial sequence (sequence3b),Nath (1977)has reported
a cheaper final sequence (sequence 3c), which has not been obtained by the new heuristic method and by the heuristic-evolutionary method of Seader and Westerberg. The latter authors and
Gomez and Seader (1976)suggested that the failure to obtain sequence 3c was due to the small, but important, effect of component
F (n-pentane) of the relative volatility for DIE (1-butane/n-butane). Finally, Table 3 shows that there is no guarantee that the
application of the global evolutionary strategy of Nath and Motard
will always improve the initial and subsequent sequences. This is
evident by noting that the third sequence (sequence 3d) is more
expensive than the second sequence (sequence 3a) during the evolutionary synthesis by the method of Nath and Motard.
Example 3 6 Separatlon of Light Oleflns and Paraffins by Ordinary
Distillation
This example has the same six-component feed mixture as in
Example 3A, and it is desired to find the sequences for separating
the feed into the following products: A , BD, C and EF (Thompson
and King, 1972). The separation sequencing can be done by using
heuristic D1 and making minor changes in step ( 4 )in the solution
to Example 3A.
(4) Heuristic C2: As in the separation sequencing for Example
3A, the split ABCIDEF is performed first. The resulting products,
ABC and DEF, are separated as follows. To separate ABC, the
difficult split B/C is done last as in the case for Example 3A. To
separate DEF, the only recommended split according to heuristic
D1 is D/EF since EF is a single produce. The other desired product
BD can be obtained by blending B and D from the preceding
separations. The resulting sequence is:
The second sequence can be systematically found by examining
the alternative splits in separating ABC, while retaining the best
initial split (accordingto CES)ABC/DEF for separating ABCDEF
and also the split D/EF which gives EF as a single product. Thus,
if the second best split according to CES in separating ABC,
namely, AB/C, is done first instead of A / B C :
f:
- 1) x loo:
(0
CES :
AlChE Journal (Vol. 29, No. 6)
&
A
20135
250
142.8
November, 1983
A S
20/35
20
11.4
Page 931
OF REPORTED SEQUENCES FOR EXAMPLE
3B
TABLE4. COMPARISON
HeuristicEvolutionary Method
(Nath & Motard, 1981)a
Ordered Heuristic
Sequence Method, This Work
3a’
3b
3c’
a
Initial Sequence
2nd Sequence
3rd Sequence
Final Sequence $600,395/yr (Best)
Algorithmic Method
HeuristicAlgorithmic Method
(Thompson & King, 1972)
(Westerberg &
Stephanopoulous,1975)
Final Sequence $694,0/yr (Rest)
Rest Sequence $602,76O/yr (Best)
2nd Best Sequence $642,068/yr (6.5%)
Initial Sequence $663,385/yr (10.5%) 2nd Rest Sequence $760,000/yr (9.5%) 3rd Best Sequence $685,632 (13.8%)
As reported in Nath (1977)
RL(1):ABCDEF
the resulting sequence is:
Since no other sequences with an initial split ABCIDEF which
satisfy the constraintsimposed by heuristicsMI to C1 are available,
the third sequence is to be found by considering the alternative
initial splits for separating ABCDEF. Specifically, if the second
best split (according to CES) in separating ABCDEF, namely,
AIBCDEF, is chosen instead of ABCIDEF, the resulting sequence
is:
Table 4 compares the sequences synthesized by several methods,
including the new heuristic method and the heuristic-evolutionary
method by Nath and Motard. It is significant to note from Table
4 that sequences 3a‘, 3b’ and 3c’ exactly correspond to the best,
second best and third best sequences, respectively, obtained by
Westerberg and Stephanopoulos (1975) using an optimization
method. Sequence 3a’ is identical to the best sequence obtained
by the heuristic-evolutionarymethod by Nath and Motard and by
the heuristic-algorithmic method by Thompson and King (1972).
Also, sequence 3a’ is cheaper than the initial sequence obtained by
the ordered heuristic method by Nath and Motard.
Example 4: n-Butyiene Purification by Ordinary and Extractive
Distillation
RL(II):ACBDEF
The desired products of the separation are the following: A , C,
BDE and F . The separation sequencing by the new heuristic
method can be done as follows.
(1) Heuristic M1: Use extractive distillation for split CIDE and
ordinary distillation for all other splits.
(2) Heuristic M2: Use low temperature and ambient to moderate pressure.
(3) Heuristic D1: Avoid splitting DE as both D and E are in the
same product, and blend together B and DE to obtain a multicomponent product BDE.
(4) Heuristic S1: Not applicable.
(5) Heuristic S2: Since split CIDE is difficult and requires extractive distillation, it should be performed last in the absence of
A , B and F .
(6) Heuristic C1: Although C is a large fraction of the feed, it
should not be separated first due to the preceding heuristic S2.
Further, it is preferred to carry out the extractive distillation for
splitting CIDE at the end of the sequence. This will avoid having
the mass separating agent as a possible contaminant in the intermediate separations of the sequence.
(7) Heuristic C2: For separating ABCDEF, split ABCIDEF is
performed last so that the remaining splits to be chosen are A /
BCDEF, ABICDEF and ABCDEIF. The latter split is chosen since
it has the largest (CES)Iof 9.406:
A
A
B
B
C/$
:\
To separate ABCDE, the possible splits are A/BCDE and AB/
CDE. Since
AIBCDE
ABICDE
1.47/92.63
16.22/77.88
f
(a- 1)x 100
145
18’
CES
2.301
3.749
split ABICDE is preferred over A/BCDE. The resulting sequence,
which splits AIB and C / D E last, is as follows:
Consider the multicomponent separations in the industrial purification of n-Butylene (Hendry and Hughes, 1972). The feed
mixture is:
Species
A:Propane
B:l-Butene
C:n-Butane
D:trans-Butene-2
E:cis-Butene-2
F:n-Pentane
&
14’75
5Q’30
15.62
11‘96
5.90
Relative
Volatilitya
w
&
2.45
1.18
1.03
1.17
1.70
2.50
(CESh (CE.911
2.163
3.485
3.29
1.510
35.25
A second sequence is obtained by splitting AIBCDE first, instead
of A BICDE :
9.406
a (a),= adlacent relative volatility at 65 6°C and 1.03 MPa for separation method I, ordinary
distillation, (-)I, = adjacent relative volatility of 65 6°C and 1 tX3 MPa for separation method 11,
extractive distillation.
The rank lists (RL)of decreasing adjacent relative volatility corresponding to separation methods I and I1 are given by:
Page 932
November, 1983
AlChE Journal (Vol. 29, No. 6)
TABLE5.
Ordered Heuristic
Sequence Method, This Work
4a
4b
4c
4d
4e
Initial Sequence
2nd Sequence
3rd Sequence
4th Sequence
5th Sequence
4f
COMPARISON OF REPORTEDSEQUENCES FOR
Algorithmic Method
(Hendry and Hughes,
1972)a
$867,400/yr (0.8%)
$878,200/yr (1.8%)
$860,400/yr (Best)
$878,000/yr (2.0%)
$872,400/yr (1.5%)
$1,095,600/yr (27.3%)
EXAMPLE
4
Heuristic-EvolutionaryMethods
Nath & Motard
Westerberg (1977)
(1981)
Seader &
Final Sequence $860,400/yr (Best)
Initial Sequence $878,000/yr (2.0%)
2nd Sequence $872,400/yr (1.5%)
Final Sequence $658,737/yr (Best)
2nd Sequence $669,844/yr (1.7%)
Initial Sequence $1,171,322/yr (77.8%)
~
As reported in Hendry (1972) and quoted in Heniey and Seader (1981, p. 547)
As there are no other sequences with an initial split ABCDEIF
which satisfy the constraints imposed by heuristics M1 to C1, the
third sequence is to be found by examining the alternative initial
splits for separating ABCDEF. Thus, if the second best initial split
for separating ABCDEF by ordinary distillation, ABICDEF, with
the second largest (CES)z of 3.485, is done first, the resulting sequence, which splits AIB and C / D E last, is:
Westerberg and by Nath and Motard, namely, sequences 4d and
4f, respectively. Based on the costs reported by Hendry (1972),
sequence 4a has only a 0.8% higher cost than that for the best sequence (4c) synthesized by the heuristic-evolutionary methods by
Seader and Westerberg and by Nath and Motard. Also, both the
new heuristic method and the ordered heuristic method by Seader
and Westerberg have generated much cheaper initial sequences
(4a and 4d) than that (4f) by the ordered heuristic method by Nath
and Motard.
CONCLUDING REMARKS
Alternatively, if the third best initial split for separating ABCDEF
by ordinary distillation AIBCDEF with the third largest (CES)z
of 2.163is performed first, two other sequences, which split CIDE
last, can be found as follows:
Note that sequence 4d is better than sequence 4e according to the
values of CES in separating BCDEF:
BCDEIF
5.90f 92.62
84.06
5.355
f
(a - 1) x 100
CES
BICDEF
14.75/83.77
24.85
4.375
Table 5 compares the sequences synthesized by different
methods for the present problem. The additional sequence (4f),
which involves replacing the split BIC in sequence 4e by extractive
distillation, is as follows:
A
A
Table 5 shows that sequence 4a is cheaper than the initial sequences obtained by the ordered heuristic methods by Seader and
AlChE Journal (Vol. 29,
No. 6)
It is important to note that although heuristic S1 (remove corrosive and hazardous components first) has not been explicitly
applied in the preceding examples, the use of this heuristic has been
shown to be important in deciding the essential first splits in many
separation sequencing problems in which feed mixtures contain
corrosive and hazardous components. Typical example problems
solved in this work have included the multicomponent separation
sequencing in the manufacture of detergents from petroleum
(Rudd et al., 1973, pp. 281-295). In this problem, it is essential to
remove the corrosive hydrogen chloride from the mixture of
chlorinated products and unreacted species (decane, monochlorodecane, dichlorodecane, chlorine and hydrogen chloride). For
this reason, heuristic S1 has been included in the new heuristic
method.
The preceding examples have shown that the initial sequences
synthesized by the new heuristic method are cheaper than those
generated by the ordered heuristic methods of Seader and
Westerberg (1977) and of Nath and Motard (1981). These initial
sequences are also either identical to or at most 2% higher in costs
than those optimum sequences obtained by other algorithmic (e.g.,
Hendry and Hughes, 1972),heuristic-algorithmic(e.g., Thompson
and King, 1972) and heuristic-evolutionary (Seader and Westerberg, 1977; Nath and Motard, 1981)methods. The only exception
is Example 3A, for which Nath (1977)has reported a final sequence
(sequence 3c) that has not been obtained by the new heuristic
method and by the heuristic-evolutionary method of Seader and
Westerberg. This final sequence is about 8.7% lower in cost than
the initial sequence (sequence3a) synthesized by the new heuristic
method. An explanation for the failure to obtain sequence 3c
suggested by Seader and Westerberg has been given previously in
Example 3A.
The new heuristic method has also been tested with many other
multicomponent separation sequencing problems reported in the
literature. The specific synthesis problems solved by the new
method have included essentially all of the problems described by
Thompson and King (1972), Westerberg and Stephanopoulos
(1975), Stephanopoulos and Westerberg (1976),Rodrigo and Seader
(1976),Gomez and Seader (1976),Seader and Westerberg (1977),
Nath (1977), and Nath and Motard (1981).Also, many test problems presented in the textbooks of Rudd et al. (1973, Chapter 5)
and Henley and Seader (1981, Chapter 14) have been solved. The
results from this work have shown essentially the same conclusion
as observed in preceding examples.
Finally, it should be pointed out that the magnitude of cost
differences for example problems, as shown in Tables 2 to 5, are
November, 1983
Page 933
relatively small. As was suggested by Tedder (1975),the magnitude
of possible round-off errors (noises)resulting from the application
of optimization techniques to separation sequencing problems with
different initial solutions could often be greater than the cost differences indicated in these tables. Under such situations, it is important to select the best sequence from several initial sequences
based on additional performance criteria other than the total cost
such as the ease of startup and shutdown, the operating temperature and pressures relative to the critical points, the overall tower
dimension, etc. The new heuristic method as presented in this work,
provides a simple and effective procedure for the systematic synthesis of good initial sequences for carrying out such a multiobjective design optimization.
ACKNOWLEDGMENT
This work was supported in part by a grant from the Engineering
Experiment Station, Auburn University. The authors would like
to thank J. D. Seader of the University of Utah, R. L. Motard of
Washington University, and D. W. Tedder of the Georgia Institute
of Technology, for their helpful comments on this paper. Special
appreciation is also extended to Motard for providing the authors
with a copy of Nath’s dissertation.
NOTATION
B
CES
CDS
D
= molal flow rate of bottoms product, mol/h
= coefficient of ease of separation defined by Eq. 1
= coefficient of difficulty of separation defined by Eq. 3
= molal flow rate of the overhead (distillate) product,
F
= molal flow rate of the feed, mol/h
= D / B or BID such that f < 1
= optimal overhead pressure, MPa
mol/h
f
PD
= split fraction of feed in a given product
= normal boiling point of a component, “C
TFB = normal bubble point of a feed stream, “C
SP
T
Greek Letters
a
= relative volatility of key components to be separated
Subscripts
LK
HK
= light key component
= heavy key component
LITERATURE CITED
Gomez, M. A,, and J D. Seader, “Separation Sequence Synthesis by a
Predictor-Based Ordered Search,” AIChE ]., 22,970 (1976).
Harbert, W. D., “Which Tower Goes Where?” Pet. Ref., 36, No. 3, 169
(1957).
Heaven, D. L., “Optimum Sequencing of Distillation Columns in Multicomponent Fractionation,” M.S. Thesis, University of California,
Berkeley (1969).
Hendry, J. E., “Computer Aided Synthesis of Optimal Multicomponent
Separation Sequences,”Ph.D. Thesis, University of Wisconsin, Madison,
WI (1972).
Hendry, J. E., and R. R. Hughes, “Generating Separation Process Flowsheets,” Chem. Eng. Prog., 68, No. 6,71 (1972).
Henley, E. J., and J. D. Seader, Equi&rium-Stage Separation Operations
in Chemical Engineering, Wiley, New York (1981).
Hohmann, E. C., M. T. Sander, and H. Dunford, “A New Approach to the
Synthesis of Multicomponent Separation Schemes,” AIChE National
Meeting, Chicago, (Nov., 1980).
King, C. J., Separation Processes, 2nd Ed., McGraw-Hill, New York
(1980).
Lockhart, F. J., “Multi-Column Distillation of Natural Gasoline,” Pet. Ref.,
26, No. 8,105 (1947).
Nath, R., “Studies in the Synthesisof Separation Processes,” Ph.D. Thesis,
The University of Houston, Houston (1977).
Nath, R., and R. L. Motard, “Evolutionary Synthesis of Separation Processes,’’ AIChE .?.,27,578 (1981).
Nishida, N., G. Stephenopoulos, and A. W. Westerberg, “A Review of
Process Synthesis,” AIChE J . , 27,321 (1981).
Nishimura, H., and Y. Hiraizumi, “Optimal System Pattern for Multicomponent Distillation Systems,” Int. Chem. Eng., 11,188 (1971)
Rathore, R. N. S., K. A.Van Wormer, and G. J. Powers, “Synthesisof Distillation Systems with Energy Integration,” AIChE I.,20,940 (1974).
Rodrigo, B. F. R., and J. D. Seader, “Synthesis of Separation Sequences by
Ordered Branch Search,” AIChE J., 21,785 (1975).
Rudd, D. F., G. J. Powers, and J. J. Siirola, Process Synthesis, Prentice-Hall,
Englewood Cliffs, NJ (1973).
Seader, J. D., and A. W. Westerberg, “A Combined Heuristic and Evolutionary Strategy for the Synthesis of Simple Separation Sequences,”
AIChE I.
23,951
, (1977).
Souders, M., “Countercurrent Separation Processes,” Cfaent.Eng. Prog.,
60,No. 2,75 (1964).
Stephanopoulos, G., and A. W. Westerberg, “Studies in Process Synthesis-11. Evolutionary Synthesis of Optimal Process Flowsheets,” Chem.
Eng. Scl., 31,195 (1976).
Tedder, D. W., “The Heuristic Synthesis and Topology of Optimal Distillation Networks,” PhD Dissertation, University of Wisconsin, Madison,
WI (1975).
Tedder, D. W., and D. F. Rudd, “Parametric Studies in Industrial Distillation. Part 11: Heuristic Optimization,” AIChE ]., 24,316 (1978).
Thompson, R. W., and C. J. King, “Systematic Synthesis of Separation
Schemes,” AIChE J . , 18,941 (1972).
Westerberg, A. W., and G. Stephenopoulous,“Studies in Chemical Process
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Synthesis of Separation Schemes,” Chem. Eng. S d . , 30,963 (1975).
Van Winkle, M., Distillation, McGraw-Hill, New York (1967).
Symbols
A
=ATor(a-l)X100
Page 934
November, 1983
Manuscript receiwd April 9, 1981; reoislon received August 5 and accepted December 14,1982.
AlChE Journal (Vol. 29, No. 6 )